1. Field of the Invention
The present invention relates to filter, in particular to filter of an adjustable frequency response.
2. Description of Related Art
Filter is an important building block in numerous systems. A filter can be implemented using either a passive circuit or an active circuit. A passive filter comprises a plurality of passive elements, including: resistor, capacitor, and inductor. An active filter comprises at least one operational amplifier and a plurality of passive elements, including resistor and capacitor. A filter receives an input signal and generates an output signal in response. The input signal is usually comprised of various frequency components, and the filter responds to different frequency components differently. The frequency dependence of a filter's response to its input is referred to as the frequency response of that filter. Based on its frequency response, a filter usually falls into one of the four categories: low-pass filter, high-pass filter, band-pass filter, and all-pass filter. A high-pass filter, for instance, has a high-pass frequency response, where high-frequency components are preserved while low-frequency components are greatly attenuated in the output, so to speak. Although the current invention is applicable to any of the four categories, a high-pass filter is used by way of example but not limitation.
A high-pass filter is characterized by a cut-off frequency. Components of frequencies well above the cut-off frequency are considered high-frequency components and will be preserved in the output, while components of frequencies well below the cut-off frequency are considered low-frequency components and will be greatly attenuated in the output. Components of frequencies near the cut-off frequency are considered transition-band components and are not well preserved nor greatly attenuated in the output.
FIG. 1 depicts a prior art passive high-pass filter 100 comprising a capacitor C and a resistor R. The cut-off frequency of this high-pass filter is 1/(2π√{square root over (RC)}), assuming the source (at the input node) has very low output impedance and the load (at the output node) has very high input impedance.
In some applications, it is necessary to adjust the frequency response of a filter while the filter is continually receiving an input signal. One common way of adjusting the frequency response of a filter on the fly is to use a tunable circuit element, e.g. a tunable resistor. A tunable circuit element can be tuned either mechanically or electronically. In an integrated circuit, a tunable circuit element can be tuned only electronically. An electronically tunable circuit element usually has poor linearity unless the tunability is based on using switch. FIG. 2 depicts a switch-based adjustable high-pass filter 200 comprising a capacitor C, a first resistor R1, a second resistor R2, and a switch S. The switch S is controlled by a logical signal (not shown in the figure). When the logical signal is in a first state, the switch S is open and the cut-off frequency of the high-pass filter 200 is 1/(2π√{square root over (R1C)}). When the logical signal is in a second state, the switch S is closed and the cut-off frequency of the high-pass filter 200 is 1/(2π√{square root over (R1R2C/(R1+R2))}), as the two resistors R1 and resistor R2 are connected in parallel and result in an effective resistance R1R2/(R1+R2).
An adjustable filter based on using a switched circuit element has a drawback that every time the switched circuit element switches from one configuration to another it introduces a disturbance to the system. The disturbance is only a transient phenomenon and will fade out eventually. However, the system suffers from a performance degrade during the transition period.
What is needed is a method to adjust the filter response without introducing a disturbance to the system.